Dual decision equalization apparatus

ABSTRACT

An adaptive equalization method and device which provides for the equalization of symbol sequences sent through fading multipath channels with time and frequency dispersion. By using a trainer system to supply an estimate of the received symbol sequence to a trainee system, equalization of the received symbol sequences is accomplished without the need for training sequences and with the ability of compensating for spectral nulls without a substantial increase in the noise in the system. The trainer system is configured as a decision directed equalizer with a feed forward filter having the received symbol sequence as input and connected to a decision element that outputs decided symbols. The trainee system is similar to decision feed back equalization in that it has a feed forward filter, a feedback filter and a decision element but, differs in that the input to the feed back filter is provided by the trainer system. The feed forward filter of the trainee system takes received symbol sequence as input. The output of the feed forward filter and the feedback filter of the trainee system is provided to the decision element which outputs the equalized symbol sequences.

This is a continuation of application Ser. No. 08/259,850 filed on 15Jun. 1994, now U.S. Pat. No. 5,539,774.

BACKGROUND OF THE INVENTION

1. Related Patent Applications

U.S. patent application Ser. No. 07/846,651 filed Mar. 5, 1992, entitled"System and Method of Estimating Equalizer Performance in the Presenceof Channel Mismatch", IBM Docket No. EN992026 and U.S. patentapplication Ser. No. 07/866,928 filed Apr. 10, 1992, entitled, "Systemand Method of Robust Sequence Estimation in the Presence of ChannelMismatch Conditions" IBM Docket No. EN992057, both assigned to the sameassignee as the present invention.

2. Field of the Invention

The present invention relates to a device and method for performingadaptive equalization in a communications system. In particular, thepresent invention provides for blind or referenced trained adaptiveequalization for use in digital communication systems.

3. Description of the Prior Art

In communications systems multiple reflections lead to a confluence at areceiver of several signals which all stem from the same signalgenerated at a transmitter but differ in arrival time, carrier phase andamplitude. This can impair the transmission performance and cause fadingor even signal elimination at the receiver. These so-called multipatheffects particularly appear in urban environments which are at the sametime those areas with the highest demand for communication systems. Therelative motion of the receiver with respect to the transmitter and/orthe transmitter with respect to the receiver can cause a doppler effectwhich can cause fading which also impairs transmission performance.These effects are particular troublesome with mobile communicationsystems. Mobile channels are generally characterized as fading multipathchannels with time dispersion (multipath spreads). The mobility of suchsystems creates transmission channel characteristics that are constantlychanging as the geometries, transmission path, interference andtransmission medium change.

The high bit or data rates of modem digital mobile radio systems cause asignificant part of the typical multipath effects to appear asinter-symbol interference (ISI). Because of the non-ideality of thefrequency response of the transmission channel, each transmitted symbolinterferes with the others, generating ISI. To remove the inter-symbolinterference, the systems are usually equipped with equalizers (seeLucky R. W., "Automatic equalization for digital communication", BellSystem Technical Journal, 1965, 44, pp. 574-588). Equalizers are widelyused in communications systems and can employ either dedicated hardwareor a programmable digital signal processors (DSP) or DSPs. There are twoprimary types of equalizers: linear and non-linear. Both types ofequalizers can be classified as either reference trained or blind. Bothtypes of equalizers typically utilize an adaptive filter. The adaptivefilter, often referred to as transversal filter or moving averagefilter, is made with a chain of delay elements, at the output of each ofwhich is placed a variable gain amplifier (tap gain). The variable tapgains are usually referred to as adjustable coefficients. The outputs ofthe variable tap gain amps are then added to provide a signal samplewhich gives an indication of the transmitted symbol. This signal sampleis then sent to a decision element or symbol detector to obtain adecided symbol. Assuming no errors, the decided symbol should be equalto the symbol fed into the transmission channel by the transmitter.

By appropriate selection of the delay elements and the coefficients,equalizers can reduce the inter-symbol interference according to a givencriterion. Some types of equalizers, referred to as adaptive, providefor automatic coefficient adjustment. In these equalizers, starting fromarbitrary initial coefficients often quite far from the optimum, thecoefficients can be modified iteratively until an optimal configurationis reached. To minimize inter-symbol interference many adaptiveequalization systems adopt the criterion of minimizing the mean squareerror (MSE) defined from the signal samples at the adaptive filteroutput before the decision element and the corresponding transmittedsignals using estimated gradient methods. For a given transmissionchannel, the mean square error is a quadratic function of the tap gainsfor referenced trained adaptive filters. The mean square error isminimized by estimating its gradient with respect to the filtercoefficients. The filter coefficients are modified in the directionopposite to the estimated gradient.

More particularly, starting from arbitrary tap gain values, differencesare found between the transmitted reference symbols and the signalsamples at the equalizer output. Using these differences, in combinationwith the signals present at the equalizer input, the tap gains aremodified to obtain the minimum mean square error. It can be shown that atap gain configuration which minimizes the mean square error exists andis unique (see Gersho A., "Adaptive equalization of highly dispersivechannels for data transmission", Bell System Technical Journal, 1969,48, pp. 55-70). When the optimum configuration has been reached theoutputs of the receiver decision element, i.e. the self-decided symbols,are correct with very high probability and can be used instead of thereference symbols to obtain the present value of the error to be used inthe adaptation process. Many other coefficient adjustment schemes havebeen suggested. The basic assumption for the adaptive equalizer istherefore that the current output samples for the adaptive equalizer canbe compared with the corresponding transmitted symbols, which have to beknown a priori.

However, if the channel characteristics change during transmission, asis particularly the case with mobile systems, the self-decided symbolsmay become incorrect and the equalizer is unable to reconfigure the tapgains to the new optimum values. In this case, to obtain reliableself-decided symbols at the receiver output, the above describedstart-up procedure (i.e., the transmitted reference sequence andadjustment of the coefficient) must be repeated with considerable lossof time. To remedy this serious drawback, blind equalization techniqueshave been proposed. Blind equalization techniques are capable ofconverging in a configuration of limited distortion without thenecessity of using a predetermined reference symbol sequence (see Y.Sato, "A method of self-recovering equalization for multi-levelamplitude-modulation systems", IEEE Transaction on Communication, Vol.COM-23, N. 6, pp. 679-682, June 1975; D. N. Godard, "Self-recoveringequalization and carrier tracking in two-dimensional data communicationsystems", IEEE Transaction on Communication, Vol. COM-28, N. 11, pp.1867-1875, November 1980; A. Benveniste and M. Goursat, "Blindequalizers", IEEE Transaction on Communication, Vol. COM-32, N. 8, pp.871-883, August 1984).

To minimize inter-symbol interference these blind techniques typicallyuse new non-convex cost functions different than the mean square errorused for the self-learning equalizer. Under weak conditions, these costfunctions characterize the inter-symbol interference sufficiently wellwhile their stochastic minimization can be performed by using locallygenerated control signals with no knowledge of the transmitted data.However, these methods of adaptive blind equalization are not fullysatisfactory because they do not converge smoothly, and particularlybecause under steady state operating conditions they maintain a veryhigh residual variance of the error signal. In other words, they do notreach the point of minimal inter-symbol interference but oscillatecontinually around the minimum. This leads to operation withunacceptable results.

Blind equalization techniques are attractive not only because theyprovide for uninterrupted data transmission (because there is no need tosend a training sequence when incorrect decisions are made or thetransmission channel characteristics change) but, also because they arequite easy to implement in practice. Most of the existing blindequalization techniques can be categorized as decision-directed-typetechniques which use a nonlinear estimator at the output of theequalizer to generate a decision-directed estimated error. This error isthen utilized to adjust the coefficients in a feed forward filter. Thus,the decision directed type equalizer uses a feed forward filter tocompensate for the non-ideal channel. However, a feed forward filter isnot very effective in equalizing channels containing spectral nulls. Inan attempt to compensate for the channel distortion, the equalizerplaces a large gain in the vicinity of the spectral null and as aconsequence significantly enhances the additive noise present in thereceived signal. Consequently, decision directed blind equalizers arenot effective for equalizing channels containing spectral nulls.Spectral nulls in the transmission channel are encountered in practicewherever there is multipath propagation. Mobil radio channels, asdiscussed above, are generally characterized as fading multipathchannels with time dispersion (multipath spreads). The ability of theequalizer to compensate for spectral nulls is particularly importantwhere multi-path propagation is present.

Additionally, a decision directed equalizer does not efficientlycompensate for postcursor ISI. Postcursor ISI is the effect ofpreviously detected symbols on the present symbol. Because detectedsymbols are not used as feedback, the effect of ISI from previouslydetected symbols is not effectively removed from the present estimate.The decision directed equalization with a feedforward filter attempts toinvert the transmission channel without directly using previouslydetected symbols.

Decision feedback equalization techniques use feedback to provide forbetter compensation for spectral nulls and attempt to eliminatepostcursor ISI. Decision feedback equalization permits the removal ofISI by using decision feedback to cancel from the present symbol theinterference from symbols which have already been detected. The basicidea of decision feedback equalization is that if the value of symbolsalready detected are known then the ISI contributed by these symbols inthe present symbol can be determined and canceled exactly by subtractingthe previously detected symbol values with appropriate weighing. Atypical decision feedback equalizer combines the output of a feedforward filter and feedback filter, and provides the combined outputs toa decision element. The output of the decision element is then utilizedby the feedback filter. The output of a feedback filter can be thoughtof as representing the postcursor ISI imposed by previously detectedsymbols on the present symbol.

The adjustment of the feed forward filter and feedback filter aretypically based on the current value of the filter coefficients and anobjective function. The objective function typically uses an errorsignal which can be defined as the difference between the symbolsequence input to the decision element and the output symbol sequence ofthe decision element. Because the error signal is based upon the outputsequence and the output sequence is used as input to the feedbackfilter, decision feedback equalizers are susceptible to decision errorpropagation. Decision error propagation can cause the equalizer to "blowup", diverge or oscillate.

The problem of decision error propagation can be explained as follows,if the decision element incorrectly decides (or detects or assigns) asymbol this incorrect symbol is provided to the feedback filter asinput. It should be noted that this incorrect decision will then beutilized by the feedback filter to compensate for postcursor ISI for anumber of present symbols (the exact number will depend upon the numberof delay elements in the feedback filter). The incorrect determinationby the decision element not only impacts the symbols provided to andpropagated in the feedback filter but, also impacts the error signalwhich is utilized by the feedback filter to adjust its coefficients. Theincorrect adjustment of the coefficients along with the incorrectsymbols used by the feedback filter causes an incorrect cancellation tobe made from the present symbol (i.e., the postcursor ISI frompreviously detected symbols is incorrectly determined). The sequenceprovided to the decision element is thus incorrect and the decisionelement is more likely to make another incorrect decision. This cyclerepeats. In severe cases decision error propagation can cause theequalizer to diverge rather than converge. Thus, the decision errorpropagates through the equalizer resulting in the equalizer notminimizing the ISI.

One proposed solution to reduce the effects of decision errorpropagation is to provide a reliability criterion for the serf-decidedsymbols that prevents updating of the adjustable coefficients when thereliability criterion is low. (See U.S. Pat. No. 4,847,797 entitledAdaptive Blind Equalization Method and Device, to Picchi et. al.) Thus abinary consent function prevents the equalizer from updating theadaptive coefficients. This technique requires the additional complexityof a consent or inhibit function. It also prevents the equalizer fromtracking changes in the transmission channel when the reliabilitycriterion is low. The propagation error still exists but, the binaryconsent function allows adaptation to proceed when the propagation erroris small and stops adaptation when the propagation error is large. Thus,this technique only stops adaptation and not the propagation error.

SUMMARY OF THE INVENTION

The object of the invention is to overcome the above mentioneddrawbacks.

It is an object of the invention to equalize received signals withoutthe need to provide training sequences.

It is an object of the invention to provide for equalization for fadingmultipath channels with time dispersion.

It is still a further object to provide equalization for channels withspectral nulls without significantly enhancing the noise.

It is an object of the invention to minimize the effect of inter-symbolinterference.

It is yet another object to reduce or eliminate the effects of decisionerror propagation.

It is an object of the invention to provide for equalization for fadingmultipath channels with time and frequency dispersion.

Accordingly, the present invention provides a device and method for theequalization of received signals or received symbol sequences. Anequalization device for the equalization of electrical signals codifiedinto symbols and transmitted on a transmission channel has a first feedforward filter with a received symbol sequence as input, the first feedforward filter having a series of delay means for delaying said receivedsymbol sequence to provide one or more delayed symbol sequences, a meansfor multiplying each of the symbol sequences by an adjustablecoefficient associated with the symbol sequence, a summation means foradding the multiplied symbol sequences to obtain signal samples; a firstdecision means for assigning a decided symbol to each signal sample fromsaid first feed forward filter using a first decision process; a secondfeed forward filter with the received symbol sequence as input, thesecond feed forward filter having a series of delay means for delayingsaid received symbol sequence to provide one or more delayed symbolsequences, a means for multiplying each of the symbol sequences by anadjustable coefficient associated with the symbol sequence; a feedbackfilter with decided symbols from the first decision means as input, thefeedback filter having a series of delay means for delaying said inputsymbols to provide one or more delayed symbol sequences, a means formultiplying each of the delayed symbol sequences by an adjustablecoefficient associated with the delayed symbol sequence; a combiner forcombining the multiplied symbol sequences from the second feed forwardfilter with the multiplied symbol sequences of the feedback filter toprovide combined signal samples; a second decision means having thecombined signal samples as input, the second decision means forassigning a decided symbol to each input signal sample using a seconddecision process, providing said decided symbol as the output of theequalizer apparatus; a first coefficient adjustment means for adjustingthe coefficients of the first feed forward filter using a firstcoefficient adaptation process and a first objective function; a secondcoefficient adjustment means for adjusting the coefficients of thesecond feed forward filter using a second coefficient adaptation processand a second objective function; and a third coefficient adjustmentmeans for adjusting the coefficients of the feedback filter using athird coefficient adaptation process and a third objective function.

An equalization method for the equalization of electrical signalscodified into symbols and transmitted on a transmission channel havingthe steps of filtering a received symbol sequence with a first feedforward filter having adjustable coefficients; assigning one or moresymbols to said filtered symbol sequence by a first decision element;filtering said received symbol sequence with a second feed forwardfilter having adjustable coefficients; filtering said assigned symbolsfrom said first decision element by a feedback filter having adjustablecoefficients;, combining said filtered symbol sequence from said secondfeed forward filter with the filtered symbol sequence from said feedbackfilter; assigning one or more symbols to said combined symbol sequenceby a second decision element and outputting said assigned symbols fromsaid second decision element as the equalized symbol sequence; andupdating the adjustable coefficients associated with the First feedforward filter, the Second feed forward filter and the feedback filter.

The present invention is an adaptive equalization method and devicewhich provides for the equalization of symbol sequences sent throughfading multipath channels with time dispersion. By using a trainersystem to supply an estimate of the received symbol sequence to atrainee system equalization of the received symbol sequences isaccomplished without the need for training sequences and with theability of compensating for spectral nulls without substantialincreasing the noise in the system. The trainer system is configured asa decision directed equalizer with a feed forward filter having thereceived symbol sequence as input and connected to a decision elementthat outputs decided symbols. The trainee system is similar to decisionfeed back equalization in that it has a feed forward filter, a feedbackfilter and a decision element but, differs in that the input to the feedback filter is provided by the trainer system. The feed forward filterof the trainee system takes received symbol sequence as input. Theoutput of the feed forward filter and the feedback filter of the traineesystem is provided to the decision element which outputs the equalizedsymbols sequences.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing and other objects, aspects and advantages of the inventionwill be better understood from the following detailed description withreference to the drawings, in which:

FIG. 1(a) depicts a typical feed forward transversal filter.

FIG. 1(b) depicts a typical feed back transversal filter.

FIG. 2 depicts decision direct equalization.

FIG. 3 depicts decision feedback equalization

FIG. 4 shows one embodiment of the present invention.

FIG. 5 shows one embodiment of the present invention highlighting theerror signals.

FIG. 6 shows one embodiment of the present invention highlighting thetrainee and trainer system elements.

FIG. 7 shows a discrete-time equivalent communication model.

FIG. 8(a) shows the scatter diagram of the distorted received signalbefore equalization.

FIG. 8(b) depicts the scatter diagram of the equalized signal using thefeed-forward only blind equalization.

FIG. 8(c) shows the scatter diagram of the equalized signal using thepresent invention.

FIG. 8(d) shows the learning curves in terms of the mean square error(MSE).

FIG. 9 shows one embodiment of the present invention using Viterbidecoding.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

I. OVERVIEW

Inherent in every communication system are channels which link atransmitter and a receiver. These channels include telephone lines usedin voice and modem applications, coaxial cables, fiber cables, underwater channels used in acoustic applications, read/write channels usedin magnetic storage devices, and atmospheric or space channels used inradar, satellite, radio, and other wireless communication systems.Although their physical media and propagation characteristics varygreatly, these channels are an important consideration in anycommunication system. A communication system consists of a transmitterfor sending symbols into a channel and a receiver for receiving thetransmitted symbols from the channel. This can be modeled as shown inFIG. 7. The equalization method and device of the present invention canbe considered as part of the receiver and offers advantages to allcommunications systems.

FIG. 4 provides an overview of the present invention. The presentinvention as depicted in FIG. 4 can be thought of as two systems: atrainer system and a trainee system. As is shown in FIG. 4 both thetrainer and trainee system receive their input signals from the samesource. The input signal is electrically coded symbols from antennae orthe front end of a receiver. The input signals can be thought of aselectrical signals which are codified into symbols. As is shown, thetrainer system consists of a decision directed equalizer having a feedforward filter and a decision element. The output signal of the trainersystem is provided as input to the feedback filter of the traineesystem. The trainee system looks similar to a decision feedbackequalizer having a feed forward filter and feedback filter with theimportant exception that the input signals for the feedback filter areprovided from the output of the trainer system instead of the output ofthe decision element of the trainee system. The output of the decisionelement in the trainee system, which is the output of the presentinvention (i.e., the equalized symbol sequence), is not directlyutilized by the trainee system. The output of the decision element ofthe trainee system may be utilized in determining one or more of theobjective functions which are used to adapt the coefficients of theadaptive filters. This feature of the present invention eliminatesdecision error propagation.

Each of the elements of the present invention is described in section IIbelow. A description of a decision feedback equalizer is also providedbecause it provides a basis for understanding the present invention andits advantageous features. A detailed description of one embodiment ofthe invention is provided in section III. One example of the expectedperformance of the present invention is provided in section V. Adiscussion of the advantages of the present invention is provided insection VI.

II. ELEMENTS

A. ADAPTIVE FILTERS

The adaptive filter is typically a finite duration impulse responsefilter with adjustable coefficients. Adjustments of the adjustablecoefficients is usually performed adaptively during the transmission ofinformation by using an objective function and a coefficient adjustmentprocess. This objective function is usually minimized or optimized bythe coefficient adjustment process. The coefficient adjustment processor adaptation algorithm adjusts the adjustable coefficients of theadaptive filter to effect the objective function. In many systems, theobjective function is an error signal and the coefficient adjustmentprocess attempts to minimize the error signal. An error signal may usethe difference between the signal input to the decision element and thesignal output by the decision element. Several coefficient adaptationprocesses/adaptation algorithms are identified below.

FIG. 1(a) shows one embodiment for a feed forward filter (FFF) where theinput is a received symbol sequence which is sent through a series ofdelay elements. The received input sequence and each of the delayedinput sequences are provided to their own variable gain amplifiers (tapgain). The variable tap gains are usually referred to as adjustablecoefficients. The received input sequence and each of the delayed inputsequences are multiplied by their respective adjustable coefficients.The outputs of the variable tap gain amps are then added to provide asignal sample which gives an indication of the transmitted symbol. Thesignal sample output of the FFF can be thought of as the estimate of thetransmitted symbol with a certain delay. The signal sample output of theFFF is referred to as the present symbol or current symbol. The additionmay be carried out by a summer, combiner or adder. This signal samplecan then be sent to a decision element or symbol detector to obtain adecided symbol. As will be described, the present invention utilizes twoFFFs one in the trainer system and one in the trainee system.

FIG 1(b) shows one embodiment for a feedback filter (FBF) where theinput is a symbol sequence which is sent through a series of delayelements. The delayed sequences are each provided with their ownvariable gain amplifiers (tap gain). The variable tap gains are usuallyreferred to as adjustable coefficients. Each of the delayed inputsequences are multiplied by their respective adjustable coefficients.The output of a FBF can be thought of as representing the estimatedpostcursor ISI due to previously assigned symbols. By canceling the ISIfrom the signal sample provided by the FFF the respective ISI isremoved. The outputs of the variable tap gain amps of the FBF are thenadded with the output from a FFF to provide a signal sample which givesan indication of the transmitted symbol with the ISI cancelled. Thefeedback filter may use the same summer or combiner or adder as the FFFor a separate summer or combiner or adder. The signal sample with theISI removed can then be sent to a decision element or symbol detector toobtain a assigned or decided symbol. The present invention utilizes asingle FBF in the trainee system.

FFF and FBF are very similar in design and structure. The maindifference between the two types of adaptive filters is where they areplaced in the equalizer and the fact that the feed back filter typicallydelays all the signal sequences while the feed forward filter provides acoefficient for the input symbol sequence without any delay. The filterscan have any number of tap gains and delay elements. The exact number ofdelay elements and associated tap gain amplifiers to use is a designdecision dependent on one or more of the following factors: themodulation scheme, expected number of multipath signals, expectedstrength of multipath signals, the time dispersion, the frequencydispersion, ambient noise and data rate.

B. DECISION DIRECT EQUALIZATION (DDE)

FIG. 2 shows an overview of the decision direct equalization (linearequalization) using an adaptive filter. The basic idea of the DDEconsists of minimizing or optimizing an objective function based uponthe decision element. The objective function typically uses an errorsignal. The error signal can be the difference between the symbolsequence input to the decision element and the symbol sequence assignedor generated by the decision element, as is shown in FIG. 2. A typicalobjective function is the mean square error (MSE) which is the expectedvalue of the square of the error signal. An input sequence is providedto the feed forward filter 201, such as is shown in FIG, 1(a), where itis passed through a series of delay elements. The input symbol sequenceand the delayed symbol sequences are each multiplied by a coefficientassociated with each of the tap gain amplifiers which perform themultiplication. The multiplied symbols are then added or combined orsummed in a adding or summing or combining element in the FFF 201.

The combined symbol sequence is then provided to a decision element 203.The decision element 203 can use a decision process to determine whichsymbol the combined symbol is to be assigned from the symbol set. Theassigned symbol (or decided symbol) is then provided as the equalizedoutput of the DDE.

A coefficient adjustment element 205 is used to update the coefficientsof the FFF 201. The coefficient adjustment element 205 uses acoefficient adjustment process to update the coefficients based on thecurrent value of the coefficients, the input symbol sequence and anerror signal (if an error signal is used by the objective function) orthe gradient of the objective function. The coefficient adjustmentelement determines and updates the coefficients.

Notice that with DDE there is no feed back of the output of the decisionelement. This is contrasted with decision feedback equalization(non-linear equalization) shown in FIG. 3 and discussed below. As alinear system the DDE basically attempts to invert the channel. As suchfor spectral nulls the DDE will place a large gain in the vicinity of aspectral null. This will in turn increase the noise in the sequence atthe output of the FFF 201. Thus, the DDE suffers from the drawback inthat it cannot provide for good compensation for spectral nulls.

Additionally, DDE does not efficiently compensate for postcursor ISI.This is primarily because assigned symbols are not directly used asfeedback, thus the effect of ISI from previously assigned symbols is noteffectively removed from the present estimate. DDE attempts to invertthe transmission channel without directly using previously detectedsymbols.

C. DECISION FEEDBACK EQUALIZATION (DFE)

DFE permits the removal of postcursor ISI by using feedback. DFEattempts to cancel the interference from symbols which have already beenassigned (or detected) from the present symbol. The basic idea of theDFE is that if the value of symbols already assigned are known then theISI contributed by these symbols can be determined and canceled exactlyby subtracting past symbol values with appropriate weighing from thepresent symbol. FIG. 3 shows one embodiment of a DFE. DFE (also referredto as non-linear equalization) uses a feed forward filter and a feedback filter. The input sequence is provided to the FFF, as is shown inFIG. 3, where it is passed through a series of delay elements. The inputsymbol sequence and the delayed symbol sequences are each multiplied bya coefficient associated with each of the tap gain amplifiers whichperform the multiplication. The multiplied symbols are then added orcombined or summed in an adding or summing or combining element. Thiselement may also combine multiplied symbols obtained from the FBF 305.Note that this element 303 is shown as separate for the FFF and FBF inFIG. 3, but it may be made part of the FFF 301 or the FBF 305 (asdepicted in FIG 1(a) and FIG 1(b) respectively) and/or used for both. Asshown in FIG. 3, the combining element 303 combines the sequence fromthe FFF 301 and subtracts the sequence provided from the FBF 305. Thecombined symbol sequence is then provided to a decision element 307.

The output of a FBF 305 can be thought of as representing the postcursorISI imposed by previous symbols on the present received symbol. Notethat the input symbol sequence to the FBF 305 is the output sequencefrom the decision element 307 (i.e., previously assigned or detectedsymbols). The FBF 305 weighs the sequence of assigned symbols toestimate the ISI in the received sequence from previously assignedsymbols. In the FBF 305 the previously assigned symbols are passedthrough a series of delay elements. The delayed assigned symbols arethen each multiplied by a coefficient associated with each of the tapgain amplifiers which perform the multiplication. The multiplied symbolsfrom the FBF 305 are then added or combined or summed in a summingelement 303 where they can be combined with the multiplied symbolsequences from the FFF 301. Note that the FBF 305 can determine thecancellation sequence or the estimated ISI (i.e., the output of the FBF305 can be added or subtracted form the output of the FFF 301). If theFBF 305 determines the cancellation sequence then the output of the FBF305 is added to the output of the FFF 301, if an estimate of the ISI isprovided then the output of the FBF 305 is subtracted from the output ofthe FFF 301. Either addition or subtraction can be used, the FBFcoefficients will converge to the correct sign accordingly. Bycompensating the received signal sequence with the output sequence ofthe FBF 305, the ISI is removed and the decision element 307 can use asequence with little or no ISI.

As was stated, the combined signals from the FFF 301 and the FBF 305 arethen provided to a decision element 307. The decision element 307determines, according to a decision process, which symbol of the symbolset the combined symbol should be assigned. The assigned symbol is thenprovided as the equalized symbol output of the DFE. The assigned symbolis also provided as input to the FBF 305 as described above for use inprocessing subsequent symbols.

A coefficient adjustment elements 311 and 309 are used to update thecoefficients in the FFF 301 and FBF 305, respectively. Each coefficientadjustment element uses a coefficient adjustment process to determinecoefficients or updates to the coefficients. As with the DDE, thecoefficient updates may be based on the current value of thecoefficients, the input symbol sequence and an error signal (if an errorsignal is used by the objective function) or the gradient of theobjective function. The coefficient adjustment element determines andupdates the coefficients. The same or different objective functions maybe used for both the FBF 305 and the FFF 301.

The coefficients for each filter are then updated according to thecoefficient adjustment process. The coefficient adjustment process istypically the same for both the FFF and FBF but may differ. Note that inthis embodiment although the coefficient adjustment process is the samethe number of coefficients (i.e., the number of tap gain amplifiers)will typically be different and the coefficient values themselves willalso be different. Various different coefficient adjustment processesare identified below.

A drawback of DFE is that it is susceptible to decision errorpropagation, particularly when multipath propagation is present in thecommunication channel. Decision error propagation stems from the DFEassuming that the decision element has correctly assigned previoussymbols. When an incorrect decision or assignment is made by thedecision element the incorrectly assigned symbol is provided to the FBF.The FBF uses the incorrectly assigned symbol in computing the postcursorISI in the present symbol. The FBF uses the incorrectly assigned symbolin determining the postcursor ISI for subsequently received symbolsuntil the incorrectly assigned symbol has propagated through all thedelay elements of the FBF. Thus, the next few received symbols areeffected as the incorrectly assigned symbol propagates through the delayelements of the FBF. The use of the incorrectly assigned symbol in turnmay create subsequent incorrect decisions because the output of the FFFis compensated for using incorrect estimate of the postcursor ISI. Thisproblem is further compounded because the error signal, used by theobjective function and the coefficient adjustment process to update theFBF coefficients, is also based upon the incorrectly assigned symbols.The incorrect adjustment of the coefficients along with the incorrectsymbols used by the feedback filter cause an incorrect cancellation tobe made from the present symbol (i.e., the postcursor ISI frompreviously assigned symbol is incorrectly determined). The sequenceprovided to the decision element is thus incorrect and the decisionelement is more likely to make another incorrect assignment which isprovided to the FBF so that the FBF is now using two incorrectlyassigned symbols. The cycle repeats and performance of the equalizerworsens as the decision error propagates through the equalizer resultingin the equalizer not minimizing the ISI.

D. COEFFICIENT ADJUSTMENT PROCESS/ADAPTATION ALGORITHM

The coefficient adjustment process determines what adjustments areneeded in the coefficients of an adaptive filter. Many adaptationtechniques have been developed. Some of these are identified below. Someadaptation algorithms require that a known sequence of symbols be sentby the transmitter in order to initially adjust the weights.Equalization schemes that do not require an initial known sequence ofsymbols or reference sequence are referred to as blind equalizationschemes. All coefficient adjustment processes make use of an objectivefunction. A typical objective function is the Mean Square Error (MSE)which uses the expected value of the square of an error signal. Thecoefficient adjustment process attempts to modify the coefficients ofthe adaptive filter such that the measure of the objective function isminimized or optimized. The coefficient adjustment process attempts tochange the coefficients so as to move closer to the minimum or optimumpoint on the objective function surface. In order to update thecoefficients the coefficient adjustment process typically determines andutilizes the gradient of the objective function with respect to thecoefficients. The following is a list of several adaptation schemes thatcan be used for updating filter coefficients:

1. Least Mean Square (LMS)-

a. Widrow & Hoff

2. Recursive Least Squares (RLS)

a. Square Root RLS

b. Fast RLS or Fast Transversal Equalization

3. Gradient

4. Katman

5. DFS

6. Zero-forcing algorithm.

7. Lattice implementations of LMS and RLS algorithms

8. Stochastic Optimization Methods (i.e., Annealing Techniques)

A survey of Adaptive Equalization Techniques is provided in "AdaptiveEqualization for TDMA Digital Mobile Radio" by John G. Proakis, IEEETransaction on Vehicular Technology, Vol. 40, No. 2, May 1991 herebyincorporated by reference. Detailed descriptions of the identifiedcoefficient adjustment processes can also be found in "Adaptive SignalProcessing" by Thomas Alexander (1986) and "Digital Communications",Second Edition 1989 by John G. Proakis, "Adaptive Filtering of NonlinearSystems with Memory by Quantized Mean Field Annealing" IEEE Transactionon Signal Processing Vol 41 No. 2, February 1993 by R. A. Nobakht et.al., all of which are hereby incorporated by reference.

The present invention is not limited to any particular adaptationtechnique, algorithm or scheme. The adaptation techniques identifiedabove are some of the more common ones. The present invention may useone or more coefficient adaptation processes in a particular embodimentof the invention. One adaptation process may be used for each adaptivefilter in the present invention. The adaptive filters may use the sameadaptation process as another adaptive filter or a different process.Each adaptive filter may have a different adaptive process or allfilters may use the same process or two filters may use the sameprocess. The particular adaptation process selected will depend upon therequirements of the communication system. Such factors as rate at whichthe transmission channel characteristics change, computationalcomplexity of a given scheme, and the capabilities of particularhardware selected for implementation will determine which particularscheme to use.

E. DECISION ELEMENT

The decision element or detection element or assignment element,determines or detects which particular symbol in a symbol set, theoutputted symbol is to be assigned. Various different decision processescan be used with the present invention. The decision element may be asimple slicer or can use a more sophisticated decision process. Theslicer may use a threshold logic function or a sigmoidal function. Otherfunctions may be utilized with the present invention as well. Thefollowing is a list of possible decision processes/algorithms:

1. Bussgang Algorithms

a) Decision directed (Lucky)

b) Generalized Dec. Directed(Karaoguz)

c) Stop-and-Go (Picchi and Prati)

d) Sato Algorithm (Sato)

e) Generalized Sate (Benveniste et. al.)

f) Bussgang (Bellini)

g) Crimno (Nikias)

h) Godard algo. (Godard)

i) CMA algo. (Treichler)

2. Polyspectra algorithms

a) Tricepstrum (Hatzinakos)

b) Power Cepstrum (Besslos et al.)

c) Cross-Tricepstrum (Brooks and Nikias)

3. Nonlinear Filter Structures

a) Volterra Series Based

b) Neural Network based (Gibson, Kohonen, Chen)

The above decision processes are well known in art and a detaileddescriptions may be found in one or more references. In particular,Adaptive Filter Theory, Second Edition by Simon Haykin herebyincorporated by reference.

FIG. 9 shows one embodiment of the present invention using a Viterbidecoder in the decision element. Viterbi decoding is particularlywell-suited when trellis code modulation is used in the transmitter. Itshould be noted that there are many ways to implement the presentinvention with viterbi decoding--the embodiment in FIG. 9 illustratingjust one embodiment of many.

The particular decision element selected will depend upon the particularcommunication system parameters, desired error rate, data rate and otherfactors. Although the present invention applies to a blind equalizationtechnique, i.e., it does not require transmission of a known training orreference sequence, it may be used with training sequences.

The present invention is not limited to any particular decision elementor decision process. The decision processes identified above are some ofthe more common ones. The present invention may use one or more decisionprocesses in a particular embodiment of the invention. The decisionelements of the present invention may use the same decision process ordifferent decision processes. The particular decision processes selectedwill depend upon the requirements of the communication system. Suchfactors as rate at which the transmission channel characteristicschange, computational complexity of a given scheme, and the capabilitiesof particular hardware selected for implementation will determine whichparticular scheme to use.

III. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

FIG. 6 shows an overview of one embodiment of the present invention. Thepresent invention is a hybrid equalization system using a DecisionDirected Equalization (DDE) section called a trainer system and amodified Decision Feedback Equalization (DFE) section called a traineesystem. As is shown in FIG. 6 the output of the trainer system 675,r_(f), is used as input to the FeedBack Filter (FBF) 605 of the traineesystem 695. In a typical DFE the output of the decision element is usedas input to the FBF. By combining a DFE and a DDE into a singleequalizer the present invention achieves significant advantages overprior art equalization techniques.

The present invention uses two equalization systems: a trainee systemand a trainer system. The trainer system is designed to continuouslytrain the trainee system without the need for training sequences. Thepresent invention in the embodiment depicted in FIG. 6 is composed offeed forward filters (FFFs), elements 601 and 603, and FBF 605. Eachfilter section can be updated using different or the same coefficientadjustment processes.

The trainer system 675 does not utilize feedback filter. The majorcomponents of the trainer system are as follows: a feed forward filter603, a decision element 613 and a coefficient adjustment element 625.The output of the trainer system is provided to the feedback filter ofthe trainee system (rf(k)). The coefficient adjustment element 625requires that an objective function be provided (e.g, MSE). The traineesystem 695 consists of a modified Decision Feedback Equalizer (DFE). Themajor components of the Trainee system 695 are as follows: feed forwardfilter 601, decision element 611, a feedback filter 605 and acoefficient adjustment element 621.

In the trainer system 675, the input to the feed forward filter 603 isthe received signal sequence, r(k). In the trainee system 695, the inputto the feed-forward filter is also the received signal sequence r(k) andthe input to the feedback filter 605 is the assigned symbols, rf(k),from the trainer system 675. The output of a FBF 605 can be thought ofas representing the postcursor ISI imposed by previous symbols on thepresent received symbol. Note that the input symbol sequence to the FBF605 is the output sequence, rf(k), from the decision element 613 (i.e.,previously assigned or detected symbols from the trainer system 675).The FBF 605 weighs the sequence of assigned symbols to estimate the ISIin the received sequence from previously assigned symbols. In the FBF605 the previously assigned symbols, rf(k), are passed through a seriesof delay elements. The delayed assigned symbols are then each multipliedby a coefficient associated with each of the tap gain amplifiers whichperform the multiplication. The multiplied symbols from the FBF 605 arethen combined with the multiplied symbol sequences from the FFF 601. Aswith DFE, the FBF 605 can determine the cancellation sequence or theestimated ISI (i.e., the output of the FBF 605 can be added orsubtracted from the output of the FFF 601). Thus, either addition orsubtraction can be used, and the FBF coefficients will converge to thecorrect sign accordingly.

For purposes of illustrating the present invention all filter sectionswill be assumed to be updated using a Least Mean Square (LMS)coefficient adjustment process. Using the LMS technique the filters areupdated in proportion to an estimated error signal (the objectivefunction). This error signal can be easily computed by an unsupervisedalgorithm.

If the complex transversal forward filter taps for the FFF 601 of thetrainee system are given as follows:

    w1=w1.sub.R +jw1.sub.I = w1.sub.0 (k)w1.sub.1 (k) . . . w1.sub.N-1 (k)!.sup.t                                                (1)

and the received complex input vector stored in the equalizer delay tapsat sampling instant k is:

    r=r.sub.R =jr.sub.1 = r(k)r(k-1) . . . r(k-N+1)!.sup.t     (2)

Then the real and imaginary components of the feed forward filter 601output, y1(k)=y1_(R) +jy1_(I), can be found as:

    y1.sub.R =r.sub.R.sup.t w1.sub.R -r.sub.I.sup.t w1.sub.I

    y1.sub.I =r.sub.I.sup.t w1.sub.R -r.sub.R.sup.t w1.sub.I   (3)

For purposes of illustrating the present invention, the decisionelements (611, 613) in FIG. 6 will be assumed to contain a nonlinearestimator represented as follows: ##EQU1## Notice that for the variancevalue, σ² =0, the nonlinearity reduces to a sign function or a "Slicer"which is equal to μ if the argument is greater than or equal to zero,and -μ if the argument is less than zero. Furthermore, the nonlinearityg(z), used by the proposed decision feed-back blind equalizationalgorithm provides a more reliable error signal than the signnonlinearity used by the classical DFE algorithm when the channeldistortion is large.

Based on the complex signal notations, the input to the nonlinearestimator of the decision element 611 can be defined as follows:

    z(k)=z.sub.R (k)+jz.sub.I (k)=y1(k)-yf(k)                  (5)

The input to the nonlinear estimator for the decision element 613 of thetrainer system can be defined as follows:

    y2(k)=y2.sub.R (k)+jy2.sub.I (k)                           (6)

The difference between the output sequence of the decision element andthe input sequence to the decision element is commonly referred to as anerror signal. The error signal is commonly used by an objectivefunction. In FIG. 6 the error signal for the trainee system can be givenas follows:

    e1(k)=g(z(k))-z(k)=e1.sub.R (k)+je1.sub.I (k), where

    e1.sub.r (k)=g(z.sub.R (k))-z.sub.R (k) e1.sub.I (k)=g(z.sub.I (k))-z.sub.I (k)                                                       (7)

and for the trainer system the error signal may be given as follows:

    e2(k)=g(y2(k))-y2(k)=e2.sub.R (k)+je2.sub.I (k), where

    e2.sub.R (k)=g(y2.sub.R (k))-y2.sub.R (k) e2.sub.I (k)=g(y2.sub.I (k))-y2.sub.I (k) g(y2(k))=rf(k)                          (8)

In the trainee system the same error signal, e1(k), is used in updatingthe feed-forward and the feedback filters. The error signal can best bedistinguished by establishing an analogy with the classical Least MeanSquares (LMS) coefficient adjustment process using the MSE as theobjective function. Observe that the complex LMS coefficient adjustmentprocess has the following update rule for the three equalizer filterswhere w1 represents the coefficients associated with FFF 601, w2represents the coefficients associated with FFF 603, and wf representsthe coefficients associated with FBF 605. Each of the coefficients foreach of the respective filters is updated as follows:

    w1(k+1)=w1(k)+α1e1(k)r*(k)

    w2(k+1)=w2(k)+α2e2(k)r*(k)

    wf(k+1)=wf(k)+αf e1(k)rf*(k)                         (9)

where (*) denotes conjugation operation and α1, α2 and αf are suitablyselected constants. Note that one constant may be used for all threefilters. α is an adapation constant or adapation rate that can bethought of as the size of the steps taken down the error curve. Othervariations of this method can be used with the present invention. Forexample the following: w(k+1)=w(k)+αe(k)r*(k)+β(w(k)-w(k-1)) whichincludes a momentum term, β(w(k)-w(k-1)), where β is a constant that ismultiplied by the change in the weights from a previous iteriation. Interms of the real and imaginary components of the complex received inputvectors, r & rf, and the error signals, e1 & e2, the update terms inequation (9) can be written as:

    r*e1=(r.sub.R e1.sub.R +r.sub.I e1.sub.I)+j(r.sub.R e1.sub.I -r.sub.I e1.sub.R)

    r*e2=(r.sub.R e2.sub.R +r.sub.I e2.sub.I)+j(r.sub.R e2.sub.I -r.sub.I e2.sub.R)

    fr*e1=(rf.sub.R e1.sub.R +rf.sub.I e1.sub.I)+j(rf.sub.R e1.sub.I -rf.sub.I e1.sub.R)                                                 (10)

Finally, all six (real and imaginary) equalizer feed-forward andfeedback filter taps are adaptively adjusted according to the followingupdate rule:

    w1.sub.R (k)+1)=w1.sub.R (k)+α1(r.sub.R e1.sub.R +r.sub.I e1.sub.I)

    w1.sub.I (k)+1)=w1.sub.I (k)+α1(r.sub.R e1.sub.I -r.sub.I e1.sub.R)

    w2.sub.R (k)+1)=w2.sub.R (k)+α2(r.sub.R e2.sub.R +r.sub.I e2.sub.I)

    w2.sub.I (k)+1)=w2.sub.I (k)+α2(r.sub.R e2.sub.I -r.sub.1 e2.sub.R)

    wf.sub.R (k+1)=wf.sub.R (k+αf(rf.sub.R e1.sub.R +rf.sub.I e1.sub.I)

    wf.sub.I (k+1)=wf.sub.I (k+αf(fr.sub.R e1.sub.I -rf.sub.I e1.sub.R)(11)

Note that while one embodiment of the present invention has beendescribed with respect to a complex notation, other implementations ofthe present invention may separate the real and the imaginary componentsfor performance purposes.

The present invention has been described for transmission ofsymbols/signals in which the sampling time and the delay introduced byeach of the delay elements of the adaptive filters are equal to thesymbol transmission time, however the present invention is perfectlyapplicable to so called fractionary equalization systems (e.g.,fractionally spaced equalization) without any significant changes. In afractionally spaced equalization only the feed forward filters w1 and w2are implemented fractionally. The FBF, wf, is not affected.

The present invention has been described without the need for thetransmitter to transmit a known symbol sequence (i.e., a reference ortraining sequence). However, the present invention may be used withtraining sequences. If training symbol sequences are used then the FBFof the trainee system is provided with the known training sequence asinput. The objective function for each of the adaptive filters wouldthen utilize the known training sequence rather than the outputs of therespective decision elements while the filters are in training mode.

Dedicated Hardware or suitable programmed Digital Signal Processor (DSP)or DSPs may be used to implement the present invention. In particularthe MWAVE Signal Processor (MSP) See the Mwave DSP 2000 series and MwaveDSP 1000 series available from IBM Corporation! may be used to implementthe present invention.

IV. EXAMPLES

The performance improvement obtained by the present invention wassimulated and compared with that of a feed forward only blind equalizer.A Quadrature Amplitude Modulation (QAM) communications system was usedto transmit symbols from a QPSK symbol alphabet in the presence ofmultipath propagation and additive white Gaussian noise. The multipathtransmission medium contains a line-of-sight (LOS) path and two othermultipaths which were one and three symbol intervals delayed. Therelative signal powers of the multipaths compared to the LOS path are0.4 and 0.2. The feed forward section of the blind equalizer consistedof 8 taps. The feedback filter had 4 taps which was adequate tocompensate for the ISI introduced by the multipaths which have a maximumof 3 symbol duration delay.

FIG. 8(a) shows the scatter diagram of the distorted received signalbefore equalization. FIG. 8(b) depicts the scatter diagram of theequalized signal using the feed forward only blind equalization (FOBE).FIG. 8(c) shows the scatter diagram of the equalized signal using thepresent invention. As can be seen from the two figures the presentinvention yields a sharper signal constellation than the FOBE. Finally,the learning curves for each are represented in FIG. 8(d) in terms ofthe mean square error (MSE). As can be seen, the present inventionattains about 15-dB improvement in the residual MSE than the FOBE.

V. ADVANTAGES AND CLOSING

The present invention provides for several significant advantages overprior art systems. The first advantage is that the present inventioneliminates the need for the transmitter to provide a training sequence.This saves communication overhead and the need to retrain when channelconditions change. Due to the blind nature of the present invention andthe trainer system, continuous self training is performed and thereforeno external training is required.

A second advantage of the present invention is that it providescompensation for spectral nulls in the transmission channel withoutsubstantially increasing the level of noise in the system. This isaccomplished by the feedback nature of the present invention. By using aDFE like structure, the trainee system avoids placing large gains in thereceived signal sequence to compensate for spectral nulls. Thus, thepresent invention provides a remedy to the inherent problem of noise,amplification for the equalization of channels containing spectralnulls.

A third advantage of the present invention is that it eliminates theproblem of decision error propagation. Because the input to the FBF ofthe trainee system is the output of the trainer system, the decisionerror propagation loop of prior art systems is broken. The output of thetrainee system is not feedback through the FBF. Therefore errors in thedecision element are not propagated back through the equalizer. Also,the DDE of the trainer system operates and is adjusted independently ofthe output of the trainee system. Thus, the present invention provides aremedy to the decision error propagation problem that has plagued otherprior art equalization techniques.

A forth advantage of the present invention is that it adapts to rapidlychanging communications channel conditions. Thus, the present inventionprovides a very attractive solution for mobile communicationsapplications where the challenging problem concerning reliabletransmission of signals through rapidly changing multipath fadingchannels with deep spectral nulls had not been resolved.

A fifth advantage is that the parallel nature of the trainer and traineesystems permits efficient parallel processor implementations. With theemergence of Digital Signal Processing and parallel computing ingeneral, comes the need to divide a solution into separate smallerproblems that do not require a lot of interaction. The present inventionwith the independence of the trainer and the trainee systems lendsitself to parallel processing implementations.

While the invention has been described in detail herein in accord withcertain preferred embodiments thereof, modifications and changes thereinmay be effected by those skilled in the art. Accordingly, it is intendedby the appended claims to cover all such modifications and changes asfall within the true spirit and scope of the invention.

What is claimed:
 1. An equalization apparatus for the equalization ofelectrical signals codified into symbols and transmitted on atransmission channel comprising:a decision direct equalizer, having afirst adaptive feed forward filter coupled to a first decision element,with a received symbol sequence as input to the first adaptive feedforward filter with the first decision element outputting a firstassigned symbol sequence; and a modified decision feedback equalizerhaving a second adaptive feed forward filter, an adaptive feedbackfilter, and a second decision element, where the received symbolsequence is input to the second adaptive feed forward filter and wherethe first assigned symbol sequence is input to the adaptive feedbackfilter and where the second decision element provides a second assignedsymbol sequence using only the combined output of the first adaptivefeed forward filter and the adaptive feedback filter.
 2. Theequalization apparatus of claim 1 wherein each decision element is aslicer.
 3. The equalization apparatus of claim 1 wherein the decisiondirect equalizer and the modified decision direct feedback equalizer areimplemented in a digital signal processor.
 4. The equalization apparatusof claim 1 wherein the second decision element of the modified decisionfeedback equalizer is a viterbi decoder.